--- title: "Fading factors and Doppler shift derivation" subject: "Wireless Communication" chapter: 3 key: "semester_7/wireless_communication:fading-factors-doppler-shift" source: https://www.bctengineer.com/q/semester_7/wireless_communication/fading-factors-doppler-shift site: BCT Engineering --- # Fading factors and Doppler shift derivation Wireless Communication · Chapter 3: Radio Wave Propagation in Mobile Networks - Asked in: 2078 Chaitra, 1+2+5 marks - Video: [Doppler Shift - Mobile Radio Propagation - Mobile Communication System](https://www.youtube.com/watch?v=nfk_9B3ZDFk) — Ekeeda - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/wireless_communication/fading-factors-doppler-shift - Whole chapter: https://www.bctengineer.com/md/semester_7/wireless_communication/chapter-3 ## Question What do you mean by fading? Explain various factors influencing small-scale fading. Derive the relation for Doppler's shift. ## Short answer Fading is rapid amplitude/phase fluctuation due to multipath interference. Factors: multipath propagation, mobile speed, surrounding objects' speed, and signal bandwidth. Doppler shift fd = (v/λ) cosθ, derived from path difference Δl = vΔt cosθ and phase change Δφ = 2πΔl/λ. ## Answer **Fading** is the rapid fluctuation of the amplitude, phase or delay of a received radio signal over a short time or travel distance, caused by interference between multiple versions of the transmitted signal (multipath) arriving at slightly different times. #### Factors influencing small-scale fading 1. **Multipath propagation:** reflecting and scattering objects create several waves with different amplitudes, phases and delays. Their vector sum varies rapidly, and the spread of delays causes time dispersion and ISI. 2. **Speed of the mobile:** motion gives each multipath component a different Doppler shift, causing random frequency modulation. Faster movement means faster fading. 3. **Speed of surrounding objects:** moving vehicles, people and doors make the channel time-varying. If objects move faster than the mobile, they dominate; otherwise they can be ignored. 4. **Transmission bandwidth of the signal:** if signal bandwidth is larger than the coherence bandwidth, the signal is distorted (frequency selective); if smaller, only its amplitude fades (flat fading). #### Derivation of Doppler shift A mobile moves with constant speed *v* from X to Y (distance *l*) in time Δt, receiving from a distant source S at angle θ to the direction of motion. ```text S (distant) / / rays nearly parallel / θ X ------------- Y → v |<---- l ----->| Δl = l cosθ ``` ```text Distance moved: l = v·Δt Path difference: Δl = l·cosθ = v·Δt·cosθ Phase change: Δφ = 2πΔl/λ = 2π·v·Δt·cosθ / λ Doppler shift: fd = (1/2π)(Δφ/Δt) fd = (v/λ)·cosθ ``` - Towards the source (θ = 0): fd = +v/λ (frequency increases). - Away from the source (θ = 180°): fd = −v/λ. - Maximum Doppler shift: fm = v/λ. **Example:** fc = 900 MHz (λ = 0.333 m), v = 72 km/h = 20 m/s → fm = 20/0.333 = 60 Hz. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. Fading is: A. Rapid fluctuation of received signal amplitude, phase or delay over short time or distance due to multipath interference B. A slow decrease of mean power with distance C. Loss due to cable attenuation D. Increase in antenna gain Answer: A. Interference between multiple delayed copies causes rapid fluctuations. (Key point: Definition of fading) 2. Which is NOT listed as a factor influencing small-scale fading? A. Multipath propagation B. Speed of the mobile C. Transmission bandwidth of the signal D. Colour of the transmitting antenna Answer: D. The factors are multipath, speed of the mobile, speed of surrounding objects and signal bandwidth. (Key point: Factors of small-scale fading) 3. In the derivation, the path difference for movement l = vΔt at angle θ is: A. Δl = l sinθ B. Δl = l cosθ = vΔt cosθ C. Δl = l/cosθ D. Δl = vΔt/λ Answer: B. Rays are nearly parallel, so the path shortens by l cosθ, giving Δφ = 2πΔl/λ. (Key point: Doppler derivation step) 4. A mobile at 20 m/s at 900 MHz (λ = 0.333 m) has maximum Doppler shift: A. 6 Hz B. 600 Hz C. 30 Hz D. 60 Hz Answer: D. fm = v/λ = 20/0.333 = 60 Hz. 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